Footage of Parliament should be freely available for use online on sites like YouTube to help "reconnect with the public", Lib Dem MP Jo Swinson said.
Footage of Commons debates is not directly downloadable
The "ridiculous" downloading ban should end to help to bring Westminster "into the 21st Century", she added.
But Nick Harvey, a member of the House of Commons Commission, said the ban was in place to ensure that images could not be "manipulated at a future point".
Current rules allow live streaming but forbid direct downloading.
'Popular and accessible'
During Commons Commission questions, Ms Swinson, MP for East Dunbartonshire, said: "Parliament should be embracing new technology as a way of reconnecting with the public, so isn't it about time we ditched the ridiculous ban on parliamentary clips being shown on YouTube?
"Sites like YouTube are popular and accessible, so if there is a copyright issue will the House authorities review the current contract [with the company that films proceedings] and bring Parliament into the 21st Century?"
Mr Harvey, who is also a Lib Dem MP, replied that copyright of the pictures was an issue, as was the cost of filming.
He said the rules dated back to when cameras were first allowed into the chamber, in the 1980s.
MPs, he added, were allowed to use clips for their own website if they showed them speaking - or a reply from a minister to their own question.
They were not permitted to show clips on "any third-party hosting website", however.
Mr Harvey said: "At the moment the rule is that the clips can be streamed to be viewed in real time, but not downloaded in such a way that they can be manipulated at a future point."
YouTube, set up in 2005, is the world's biggest video-sharing website.